Nonlinear Dynamics - The dynamic response of long lines Is very compli- 

 cated and may produce significantly different effects from those Implied 

 by the static responses. There may be significant coupling between 

 mooring, buoy and ship responses. One should expect various forms of 

 harmonic coupling. Thus, excitation at a single frequency may produce 

 responses at other frequencies. Subharmonlc responses are common and 

 super-harmonic responses are possible. Damping and large amplitude/low 

 frequency forces (drift forces and swells) are also Important factors. 



It should be noted that most moored ship analyses assume the lines are non- 

 dynamic components modeled by a simple spring which is usually assumed to be 

 linear. In some cases, a material nonllnearlty has been introduced, but most 

 other nonllnearities of the lines are ignored. Typically these analyses are 

 conducted with 6 degrees of freedom (the rigid body components of the ship) 

 and some limit the model to 3 degrees of freedom. 



Finite Element Modeling of Mooring Lines 



The finite element method offers an approach to representing the dynamic 

 equations of the lines. It is a discrete approach which uses a finite set of 

 nodal degrees of freedom to approximate the line behavior. The finite element 

 method can be viewed as a special form of the Rayleigh-Rltz method where the 

 assiomed response functions are defined in finite sub-regions rather than on the 

 entire body. Admissibility is readily assured when the assumed functions are 

 displacement fields. The finite element approach using assumed displacement 

 fields is known as the stiffness method. 



Application of the stiffness method to the modeling of mooring lines 

 requires the assumption of the geometric form as well as the displacement field 



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